LINEAR-STABILITY OF A LAYERED FLUID WITH MOBILE SURFACE PLATES

We develop a general method of calculating the linear stability of a f luid with homogeneous layers that is heated from below. The method emp loys a propagator technique to obtain expressions for the fluid veloci ty, stress, and temperature. The principal advantage of the method is the ease with which solutions are adapted to a wide variety of boundar y conditions and fluid properties. We demonstrate the utility of the m ethod using three examples which quantify the effects of (1) theologic al layering, (2) mobile plates at the surface, and (3) multiple phase transitions. Each example is presented in the context of Earth's mantl e. In the first example, we predict that convection becomes confined t o the upper mantle once the viscosity increase between the upper and l ower mantle exceeds a factor of 2000, consistent with the nonlinear ca lculations of Davies (1977). In the second example we find that the he at flux variations in a convecting fluid with variably sized, surface plates (Gable et al., 1991) can be attributed, in part, to changes in the critical Rayleigh number. The linear stability of a fluid with mul tiple phase transitions is significantly affected by the locations of the transitions. We find that phase transitions have their largest eff ect when they are located at the center of the fluid layer and become much less important when they are located near the exterior boundaries .